Simplify the following expression: $p = \dfrac{-10q^2}{20q^3 + 100q^2}$ You can assume $q \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-10q^2 = - (2\cdot5 \cdot q \cdot q)$ The denominator can be factored: $20q^3 + 100q^2 = (2\cdot2\cdot5 \cdot q \cdot q \cdot q) + (2\cdot2\cdot5\cdot5 \cdot q \cdot q)$ The greatest common factor of all the terms is $10q^2$ Factoring out $10q^2$ gives us: $p = \dfrac{(10q^2)(-1)}{(10q^2)(2q + 10)}$ Dividing both the numerator and denominator by $10q^2$ gives: $p = \dfrac{-1}{2q + 10}$